A cylindrical syringe has a height of 6.8 cm and a diameter of 2.37 cm is going to be

Mathematics

1 answer:

alukav5142 [94]3 years ago

7 0

Answer:

The number of syringe filled with water that would be needed to fill the semi-sphere is approximately 8.714 syringes

Step-by-step explanation:

The height of the syringe = 6.8 cm

The diameter of the syringe = 2.37 cm

The circumference of the hemisphere = 31.4 cm

Let r represent the radius of the hemisphere, we have;

2·π·r = 31.4 cm

r = 31.4/(2 × π) ≈ 4.9975 cm

The volume of the hemisphere = 2/3 × π × r³ = 2/3 × π × (31.4/(2 × π))³ ≈ 261.4 cm³

The volume of the syringe = π × d²/4 × h = π × 2.37²/4 × 6.8 ≈ 29.998 cm³

The number of syringe filled with water that would be needed to fill the semi-sphere = (The volume of the hemisphere)/(The volume of the syringe)

Therefore;

The number of syringe filled with water that would be needed to fill the semi-sphere = 261.4 cm³/(29.998 cm³) ≈ 8.714 syringes.

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A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t

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Full Question

A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass—spring system is disturbed from its rest state by the force F (t) = 20 cos(8t). The force F (t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.

Determine the spring constant k.

Answer:

Spring Constant = 1000Nm^-1

Step-by-step explanation:

Given

Mass = 10kg

Spring Extension = 9.8cm

Spring Constant K = Force/Extension

Force = Mass * Acceleration

Force = 10 * 9.8 = 9.8N

Spring Extension = 9.8 cm = 9.8 /100 = 0.098 m

Spring constant = 98 / 0.098